DMFT: From Infinite Dimensions to Real Materials: Lecture Notes of the Autumn School on Correlated Electrons 2018 ; Forschungszentrum Jülich, 17-21 September 2018

Since the beginning of quantum mechanics, emergent many-body phenomena represent the
grand-challenge in theoretical condensed-matter physics. Indeed, static mean-field approaches
fail to capture even the simplest many-body effects, while diagrammatic techniques generally
fail in the regime characteristic of strong correlations. The introduction of dynamical mean-
field theory (DMFT) has revolutionized this field. Two insights paved the way to this paradigm
shift. The first is that in the limit of infinite dimensions all contributions to the self-energy
become local. The second is that the locality of the self-energy makes it possible to build a new
type of mean-field theory, dynamical in nature, by mapping a correlated lattice problem onto
a self-consistent quantum-impurity model. In the last decades, thanks to advances in model
building combined with the development of flexible and numerically exact quantum-impurity
solvers, DMFT was successfully linked with ab-initio density-functional techniques, making it
the method of choice for the investigation of correlated electron materials.
This year’s school covers the most important aspects of the DMFT approach to real mate-
rials. Lectures range from the basics to advanced topics, covering the DFT+DMFT method,
non-local extensions of DMFT, advanced quantum impurity solvers, the calculation of dynam-
ical response functions, and the description of correlation effects out of equilibrium. The goal
of the school is to introduce advanced graduate students and up to this modern method for the
realistic modeling of strongly correlated matter.